My husband and I are in the early stages of planning a trip to France & Italy next year May/June for roughly 2-3 weeks
The top places we would like to visit are Paris, Monaco, Rome & Almafi coast.
Does visiting these places sound possible in this amount of time ?
what is the best way to travel between each place ?

Yes feasible
Best way, well for me the train. look at seat61.com to understand how it all works. Best way for you, no idea, it depends how you like to travel. I tend to take a picnic onboard and chat to other customers, very relaxed and lots to look at.

Unless you like to look at fossil fuel car racing I'm not sure why you want to go to Monaco but if you give us a clue we might be able to help

I'd book an openjaw and fly into Paris and out of Rome or the other way around depending on you airport connections etc

Welcome to Fodors

There really is more to do in Nice than Monaco, except if you will be splurging on the Hotel de Paris Monte-Carlo:

https://www.montecarlosbm.com/fr/hot...is-monte-carlo

1. I always suggest going to the further most destination first, so fly to Rome and visit there,
2. then train to Salerno* and hire a driver to take you to your preferred Amalfi Coast town.
3. After your Amalfi visit, taxi to Naples...either to the airport or the train station. Train or fly to Nice. Monaco is about a 25-minute ride from Nice. If you take the train, Monaco would be a stop before Nice. The train ride from Naples is loooong but you could stop along the route to break it up.
4. Take the train from Nice to Paris and fly home from there.

*Alternately, you could train to Naples....others with first-hand info can say which is best.

Here's to more first-hand corrections or alternative solutions.